The rift reflects the fundamental changes sweeping through American intelligence agencies as the C.I.A. and the F.B.I., as well as elements of the Defense Department, face increasing pressures to improve their intelligence capabilities in the aftermath of the September 2001 attacks. All three agencies are still struggling to grapple with the transformation in the threats facing the United States since the end of the cold war and are due to report to the White House next week on their plans to improve counterterrorism efforts.

In a departure from past practice, the F.B.I. wants to manage the foreigners it recruits under the new program after they return to their home countries. The C.I.A. wants to maintain its lead role in recruiting and managing these sources. The transformation of the F.B.I. into an agency that collects intelligence overseas is causing unease within the C.I.A., where officials question whether the F.B.I. has the expertise to play that role.

Among the particular sources of friction in the last year have been several episodes in which senior intelligence officials said the F.B.I. failed to inform the C.I.A. fully about its relationships with intelligence sources overseas or practiced poor tradecraft in its dealing with them.

F.B.I. officials acknowledged lapses, but said there were also instances in which the C.I.A. had failed to keep the bureau fully informed of its activities. Those problems, the officials said, underscored the necessity of reaching a new understanding.

In interviews, senior officials on opposite sides of the debate laid out their views in stark terms.

"Today the C.I.A. is the only one who can handle the overseas mission," an intelligence official said. "The C.I.A. hires and trains people to be intelligence officers; the F.B.I. hires and trains people to be law enforcement officers. They flash a badge and say, 'Tell me what I need to know,' and that gets you nowhere outside the United States."

F.B.I. officials said that agents were now being trained as intelligence officers and that the threats confronting the United States were too serious and varied to be left to one agency.

"The C.I.A. says we should just stay in our own lanes," a senior F.B.I. official said. "We think we both need to be in the same lane on a coordinated basis."

At the heart of the issue is an F.B.I. effort to expand its recruitment of foreigners visiting or living in United States, among them students, scientists and business representatives. The effort is aimed at people from traditional adversaries like the former Eastern bloc states as well as from Middle Eastern countries that are home to Islamic extremists. Other targets include citizens from a diverse array of countries like China, India, Israel, Japan, Pakistan and Taiwan.

The tension over the issue has played out in recent weeks in an exchange of communications between Porter J. Goss, the director of central intelligence, and Robert S. Mueller III, director of the F.B.I. The two have exchanged letters and proposed memorandums of understanding intended to make formal the relationship between their agencies, which in the past have often feuded over turf and viewed each other with suspicion and sometimes disdain.

Representatives from the agencies are negotiating a new arrangement that focuses on rules for the recruiting of foreigners in the United States, senior government officials said. But a final agreement is not expected until the Bush administration appoints a director of national intelligence. That post, which was created in the measure President Bush signed into law late last year, carries the responsibility of acting as a referee in such disputes.

The Los Angeles Times and The Washington Post have reported the tension between the two agencies as well as their efforts to reach an agreement about the division of domestic responsibilities. The fact that the dispute has been inflamed by conflicts overseas was described by former intelligence officials. Asked about those claims, a Bush administration official acknowledged that "some sloppiness" had contributed to the tensions.

F.B.I. officials have sought to play down the significance of any disagreements with the C.I.A., saying the bureau has long had the legal authority to recruit foreigners. The F.B.I. officials say they have been under heavy pressure to move beyond the bureau's traditional focus on specific cases to expand its ability to gather intelligence.

The two agencies have worked closely together on counterterrorism matters since the Sept. 11 attacks, and that arena is not the main focus of the current dispute, which centers on counterintelligence. Even so, in the world after the cold war, the distinctions between counterespionage and counterterrorism are increasingly blurry, and the same source could provide information useful to law enforcement, counterespionage and counterterrorism officials.

"We're not trying to say that the C.I.A. has no role or that we're trying to take it over," a senior F.B.I. official said. "We want to work in a partnership with the C.I.A. - not to add new responsibilities to the F.B.I. but to do what the F.B.I. is supposed to do."

By law the C.I.A. is barred from spying on Americans in the United States. But the agency legally recruits citizens and foreigners in the United States as sources through its relatively small network of station chiefs in the United States.

The F.B.I. has long also recruited foreigners on American soil. But now the bureau has greatly expanded its reach, establishing, for the first time, squads in each of the country's 56 field offices to identify potential recruits from the tens of thousands people working at potentially sensitive locations like university laboratories, research institutions and defense plants that might be targets for foreign intelligence efforts.

The changes that have promoted the F.B.I.'s role in intelligence gathering have caused some unease because they directly affect the day-to-day work of intelligence officers. That is in contrast to other broad changes being put into effect in response to the intelligence reorganization legislation approved by Congress last December, which drew on findings by the independent commission that examined the intelligence failures by the F.B.I, the C.I.A. and other agencies before the Sept. 11 attacks.

"This is the equivalent of asking the C.I.A. to investigate a crime scene," an intelligence official said of the F.B.I.'s efforts to play a broader role in gathering intelligence. "A C.I.A. officer doesn't know where to put the yellow tape, just as an F.B.I. agent isn't trained in handling a clandestine asset."